I own an 87 Sovereign. It has 4 red taillights - 2 on each side. My tow vehicle has daytime running lights so the taillights are always on. All 4 of the taillights glow fine when I'm not using the brakes or turn signals. When I put my foot on the brakes the left side works properly - both of the taillights glow brighter. On the right side the outside taillight glows brighter but the inside taillight goes out. When I turn on the left turn signal both taillights blink in unison. When I turn on the right turn signal the lights alternate - when the inside light is on the outside light is off and vice versa.

I don't think the tail lights are supposed to come on with the daytime driving lights (at least on my GM tv). If it is a GM the driving lights are seperate from the lighting system and head and tail lights should not come on until dark, or if the sensor on the dash is covered by something. I don't know if your tv/as worked together in the past, but if they have not been used together previously the wireing may not be the same on both vehicles. Otherwise, the previously mentioned bad bulb or ground is a good place to start.